More generally, one can show that \(\Omega _\star (\gamma )=0\)  unless the support of \(\gamma \)  (defined as the set of vertices \(i\in Q_0\)  such that \(n_i\ne 0\) ) is strongly connected
[1]}. For quivers associated to non-compact Calabi-Yau threefolds, it is conjectured in [2]}, [1]}, [4]} that
\(\Omega _\star (\gamma )=0\)  unless \(\gamma \)  belongs to the kernel of the antisymmetrized Euler form.
